GCSE Maths · Topic guide
GCSE Maths graphs revision
Graph questions test plotting skills, reading intercepts and gradients, and linking equations to shapes (straight line, parabola, etc.). 'Gradient' is rise ÷ run; parallel lines share m, perpendicular lines have m₁m₂ = −1 (Higher). When sketching, show intercepts with axes where they're easy to find. Calculator papers may ask for coordinates of turning points from a given graph or equation.
Common mistakes in exams
- Plotting without a sensible scale — points look wrong.
- Reading gradient as Δx/Δy instead of Δy/Δx.
- Confusing y-intercept with x-intercept.
- Assuming all curves are symmetric without checking the equation.
Worked examples & mini quiz
GCSE Maths: Graphs
Straight line: y = mx + c — m is gradient, c is y-intercept. Quadratic y = ax² + bx + c: U or ∩ shape from sign of a. Read solutions to f(x) = 0 as x-values where the graph crosses the x-axis.
Worked examples
Example 1
Gradient from two points (0,2) and (4,10)
m = (10 − 2)/(4 − 0) = 8/4 = 2.
Example 2
y-intercept
For y = −3x + 7, intercept is (0, 7).
Mini quiz (3 questions)
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1. The gradient of y = 4x − 1 is:
- A.4
- B.−1
- C.3
- D.1/4
Show answer
Correct: 4
y = mx + c → m = 4.
2. A parabola y = x² − 4x opens:
- A.Upwards
- B.Downwards
- C.Sideways
- D.Not a parabola
Show answer
Correct: Upwards
Coefficient of x² is positive.
3. Where does y = 2x + 6 cross the x-axis?
- A.(−3, 0)
- B.(3, 0)
- C.(0, 6)
- D.(6, 0)
Show answer
Correct: (−3, 0)
Set y = 0: 2x = −6 → x = −3.
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